Joint Probability of Wave Period and Height

The Statistics of the zero-crossing wave period as a function of wave height, i.e., the conditional probability, is important in ocean engineering, particularly for the selection of a design value of wave height and associated period for offshore installations. The derivation for the conditional probability of the wave period was given in Ref. 1, but this derivation was based on assumptions that are too restrictive for the general application to ocean waves. In the following, a derivation is given for the conditional probability of wave period and height that is based on assumptions that are less restrictive than those used in Ref 1.